Quotients of Lie Groups
If G is a Lie group and N is a normal Lie subgroup of G, the quotient G / N is also a Lie group. In this case, the original group G has the structure of a fiber bundle (specifically, a principal N-bundle), with base space G / N and fiber N.
For a non-normal Lie subgroup N, the space G / N of left cosets is not a group, but simply a differentiable manifold on which G acts. The result is known as a homogeneous space.
Read more about this topic: Quotient Group
Famous quotes containing the words lie and/or groups:
“You see, a person of my acquaintance used to divide people into three categories: those who would prefer to have nothing to hide than have to lie, those who would rather lie than have nothing to hide, and finally those who love both lies and secrets.”
—Albert Camus (1913–1960)
“Trees appeared in groups and singly, revolving coolly and blandly, displaying the latest fashions. The blue dampness of a ravine. A memory of love, disguised as a meadow. Wispy clouds—the greyhounds of heaven.”
—Vladimir Nabokov (1899–1977)